Advertisements
Advertisements
प्रश्न
Prove the following identity :
`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`
Advertisements
उत्तर
LHS = `(1 - tanA)^2 + (1 + tanA)^2`
= `1 + tan^2A - 2tanA + 1 + tan^2A + 2tanA`
= `2(1 + tan^2A) = 2sec^2A` = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
Define an identity.
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
